Comment 2 for bug 1680333

Thanks, @Mc for that info.
Maybe another example which might help to identify the detailed origin:

When rescaling objects and let them snap to existing fixed and unchanged nodes you also will get "arbitrary random numbers".
More info:
http://www.inkscapeforum.com/viewtopic.php?f=5&t=32113

...looks like there is a quantisation of the "arbitrary" numbers of 1.907348e-6 which is 2^-19. Whatever that means... and wherever it comes from...